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Example 8 - Find matrix X, such that 2A + 3X = 5B - Addition/ subtraction  of matrices

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise
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Example 8 If A = [■8(8&0@4&−2@3&6)] and B = [■8(2&−2@4&2@−5&1)] then find the matrix X, such that 2A + 3X = 5B. Given that 2A + 3X = 5B Putting values 2 [■8(8& 0@4&−2@3& 6)] + 3X = 5 [■8( 2&−2@ 4& 2@−5& 1)] [■8(8×2 & 0×2@4×2&−2×2@3×2& 6×2)] + 3X = [■8( 2×5 &−2×5@ 4×5& 2×5@−5×5& 1×5)] [■8(16& 0@8& −4@6& 12)] + 3X = [■8( 10&−10@ 20& 10@−25& 5)] 3X = [■8(10&−10@20&10@−25&5)] – [■8(16& 0@8&−4@6&12)] 3X = [■8( 10−16&−10−0@ 20−8&10−(−4)@−25−6& 5−12)] 3X = [■8( −6&−10@ 12& 14@−31& −7)] X = 1/3 [■8( −6&−10@ 12& 14@−31& −7)] = [■8((−6)/3&(−10)/3@(−12)/3&14/3@(−31)/3&(−7)/3)] = [■8(−2&(−10)/3@4&14/3@(−31)/3&(−7)/3)] Hence, X = [■8(−2&(−10)/3@4&14/3@(−31)/3&(−7)/3)]

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